Polymers

Q1 (12 marks)

(a) Definitions (3) $\bar{M}_n = \frac{\sum N_i M_i}{\sum N_i} \quad (1.5)$ $\bar{M}_w = \frac{\sum N_i M_i^2}{\sum N_i M_i} \quad (1.5)$ Why: $\bar M_n$ weights by number of molecules (mole fraction); $\bar M_w$ weights each molecule by its own mass, so heavy chains count more.

(b) Data: $N_1=4, M_1=10^4$; $N_2=1, M_2=10^5$. (6)

$\sum N_i = 5$ $\sum N_i M_i = 4(10^4)+1(10^5) = 40{,}000+100{,}000 = 140{,}000$ $\bar{M}_n = \frac{140{,}000}{5} = 28{,}000\ \text{g/mol} \quad (3)$

$\sum N_i M_i^2 = 4(10^4)^2 + 1(10^5)^2 = 4\times10^8 + 1\times10^{10} = 1.04\times10^{10}$ $\bar{M}_w = \frac{1.04\times10^{10}}{140{,}000} = 74{,}285.7\ \text{g/mol} \quad (3)$

(c) PDI (3) $\text{PDI} = \frac{\bar{M}_w}{\bar{M}_n} = \frac{74{,}285.7}{28{,}000} = 2.653 \quad (2)$ Since PDI > 1, the sample is polydisperse (broad distribution of chain lengths). A value ~2.65 indicates significant heterogeneity dominated by a few very heavy chains. (1)

Q2 (10 marks)

(a) (6 marks) — 2 marks each stage

Initiation: $(\text{C}_6\text{H}_5\text{COO})_2 \xrightarrow{\Delta} 2\,\text{C}_6\text{H}_5\text{COO}^\bullet \rightarrow 2\,\text{C}_6\text{H}_5^\bullet + 2\text{CO}_2$; radical $\text{R}^\bullet$ adds to $\text{CH}_2=\text{CHPh}$ giving $\text{R–CH}_2–\overset{\bullet}{\text{C}}\text{HPh}$. Propagation: radical adds successively to monomer: $\text{...CH}_2–\overset{\bullet}{\text{C}}\text{HPh} + \text{CH}_2=\text{CHPh} \rightarrow \text{...CH}_2–\text{CHPh–CH}_2–\overset{\bullet}{\text{C}}\text{HPh}$. Termination: combination $2\,\text{R}^\bullet \rightarrow \text{R–R}$ (or disproportionation).

(b) (2) The radical adds to the $\text{CH}_2$ (less-substituted) end so the unpaired electron sits on the carbon bearing the phenyl group — a benzylic radical stabilized by resonance with the ring; adding at that carbon is also less sterically hindered. This regioselectivity repeats, giving head-to-tail chains.

(c) (2) Combination: two growing radicals couple into one dead chain → doubles molecular weight. Disproportionation: H-atom transfer gives two dead chains (one saturated, one with terminal C=C) of lower MW. Combination gives higher molecular weight. (1+1)

Q3 (10 marks)

(a) (4) Nylon-6,6 repeat unit: $-[\text{NH}-(\text{CH}_2)_6-\text{NH}-\text{CO}-(\text{CH}_2)_4-\text{CO}]-$ Monomers: hexamethylenediamine (–NH₂ groups) + adipic acid (–COOH groups). Amide (peptide) linkage forms; water eliminated. (2 structure + 1 monomers + 1 by-product)

(b) (3) PET repeat unit: $-[\text{O}-\text{CH}_2\text{CH}_2-\text{O}-\text{CO}-\text{C}_6\text{H}_4-\text{CO}]-$ Monomers: ethylene glycol + terephthalic acid (or dimethyl terephthalate). Ester linkage. (2 structure + 1 monomers)

(c) (3) Both are polyamides of a diamine + terephthalic/isophthalic acid. Kevlar = poly(para-phenylene terephthalamide): all-para linkages → rigid, rod-like linear chains that align and H-bond into ordered sheets → very high tensile strength. Nomex = meta-substituted → kinked chains, less ordered, so not as strong but excellent thermal/flame resistance. Kevlar's para geometry + interchain H-bonding gives the axial strength needed for body armour.

Q4 (8 marks)

(a) Bakelite: condensation; thermosetting (3-D cross-linked); copolymer (phenol + formaldehyde). (2) (b) PVC: addition; thermoplastic; homopolymer (vinyl chloride). (2) (c) Nylon-6,6: condensation; thermoplastic; copolymer (two different monomers). (2) (d) Melamine–formaldehyde: condensation; thermosetting (cross-linked network); copolymer. (2)

(1 mark each = axis classifications; 1 mark each = correct justification/monomer note)

Q5 (6 marks)

(a) (3) Catalyst: triethylaluminium $\text{Al(C}_2\text{H}_5)_3$ + titanium tetrachloride $\text{TiCl}_4$ (Ziegler–Natta). It is a chain-growth coordination polymerization: monomer coordinates to the vacant site on the transition-metal centre, then inserts into the metal–carbon bond (migratory insertion). (catalyst 1.5 + mechanism/coordination 1.5)

(b) (3) Ziegler–Natta gives linear, unbranched chains that pack closely and crystallize → higher density, higher tensile strength and melting point (HDPE). Free-radical high-pressure route causes chain-transfer/back-biting → branched chains that pack poorly → lower density, lower strength (LDPE).

Q6 (4 marks)

(a) (2) PHBV = copolymer of 3-hydroxybutanoic acid and 3-hydroxypentanoic (3-hydroxyvaleric) acid. Biodegradable because it contains hydrolysable ester linkages broken down by microorganisms/enzymes. (1 monomers + 1 reason)

(b) (2) High-temperature service: polyimides (retain properties at very high T) or Nomex (flame resistance). Composite matrix: epoxy resins (strong adhesion, cross-link into rigid CFRP/GFRP matrix). (1 + 1 with property)

[
  {"claim":"Mn = 28000 g/mol for the two-species sample","code":"N1,M1,N2,M2=4,10000,1,100000; Mn=(N1*M1+N2*M2)/(N1+N2); result = Mn==28000"},
  {"claim":"Mw = 74285.71... g/mol","code":"N1,M1,N2,M2=4,10000,1,100000; Mw=(N1*M1**2+N2*M2**2)/(N1*M1+N2*M2); result = simplify(Mw - Rational(1040000,14))==0"},
  {"claim":"PDI approx 2.653","code":"N1,M1,N2,M2=4,10000,1,100000; Mn=(N1*M1+N2*M2)/(N1+N2); Mw=(N1*M1**2+N2*M2**2)/(N1*M1+N2*M2); PDI=Mw/Mn; result = abs(float(PDI)-2.6531)<0.01"},
  {"claim":"Sum of NiMi = 140000","code":"result = (4*10000+1*100000)==140000"}
]